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Question Number 158191 by ghakhan88 last updated on 31/Oct/21

Can we reach to (m/((m−1)s)) + ((m+1)/(ms^2 )) from         ((ms+m(m+1))/(s(m−s))) ??

$${Can}\:{we}\:{reach}\:{to}\:\frac{{m}}{\left({m}−\mathrm{1}\right){s}}\:+\:\frac{{m}+\mathrm{1}}{{ms}^{\mathrm{2}} }\:{from}\: \\ $$$$ \\ $$$$\:\:\:\:\frac{{ms}+{m}\left({m}+\mathrm{1}\right)}{{s}\left({m}−{s}\right)}\:?? \\ $$

Commented by Rasheed.Sindhi last updated on 01/Nov/21

They′re not equal even!  for m=2 & s=1 they have different  values.   (m/((m−1)s)) + ((m+1)/(ms^2 )) =^(?) ((ms+m(m+1))/(s(m−s)))   (2/((2−1)(1))) + ((2+1)/(2(1^2 ))) =^(?) ((2(1)+2(2+1))/(1(2−1)))   (2/1) + (3/2) =^(?) ((2+2(3))/(2−1))    (7/2) =^(?) ((2+6)/1)  (7/2)≠8

$$\mathcal{T}{hey}'{re}\:{not}\:{equal}\:{even}! \\ $$$${for}\:{m}=\mathrm{2}\:\&\:{s}=\mathrm{1}\:{they}\:{have}\:{different} \\ $$$${values}. \\ $$$$\:\frac{{m}}{\left({m}−\mathrm{1}\right){s}}\:+\:\frac{{m}+\mathrm{1}}{{ms}^{\mathrm{2}} }\:\overset{?} {=}\frac{{ms}+{m}\left({m}+\mathrm{1}\right)}{{s}\left({m}−{s}\right)} \\ $$$$\:\frac{\mathrm{2}}{\left(\mathrm{2}−\mathrm{1}\right)\left(\mathrm{1}\right)}\:+\:\frac{\mathrm{2}+\mathrm{1}}{\mathrm{2}\left(\mathrm{1}^{\mathrm{2}} \right)}\:\overset{?} {=}\frac{\mathrm{2}\left(\mathrm{1}\right)+\mathrm{2}\left(\mathrm{2}+\mathrm{1}\right)}{\mathrm{1}\left(\mathrm{2}−\mathrm{1}\right)} \\ $$$$\:\frac{\mathrm{2}}{\mathrm{1}}\:+\:\frac{\mathrm{3}}{\mathrm{2}}\overset{?} {\:=}\frac{\mathrm{2}+\mathrm{2}\left(\mathrm{3}\right)}{\mathrm{2}−\mathrm{1}} \\ $$$$\:\:\frac{\mathrm{7}}{\mathrm{2}}\:\overset{?} {=}\frac{\mathrm{2}+\mathrm{6}}{\mathrm{1}} \\ $$$$\frac{\mathrm{7}}{\mathrm{2}}\neq\mathrm{8} \\ $$

Answered by MJS_new last updated on 31/Oct/21

no

$$\mathrm{no} \\ $$

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